
where \(l^i\) , \(D\) , \(d^j\) , \(\omega \) , \(\Gamma (\cdot )\)  are the cluster index of \(i\) -th data, the number of total data, the number of data assigned to \(j\) -th cluster, concentration parameter, and gamma function respectively. The uppercase \(J\)  is used to represent the total number of clusters.
DP makes it possible for \(J\)  to represent a varying number of clusters, whether finite or infinite.
By using Eq. (REF ), a conditional prior for \(l^i\)  when all indicators other than \(l^i\)  are given can be easily calculated as [1]}
\(p(l^i=j|\mathbf {l}^{-i},\omega ) = \frac{d^{j}+\omega /J}{D-1+\omega },\) 
